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arXiv · 1308.4061

Quantum Quench and Double Trace Couplings

Pallab Basu·Diptarka Das·Sumit R. Das·Krishnendu Sengupta
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Abstract

We consider quantum quench by a time dependent double trace coupling in a strongly coupled large N field theory which has a gravity dual via the AdS/CFT correspondence. The bulk theory contains a self coupled neutral scalar field coupled to gravity with negative cosmological constant. We study the scalar dynamics in the probe approximation in two backgrounds: AdS soliton and AdS black brane. In either case we find that in equilibrium there is a critical phase transition at a {\em negative} value of the double trace coupling $κ$ below which the scalar condenses. For a slowly varying homogeneous time dependent coupling crossing the critical point, we show that the dynamics in the critical region is dominated by a single mode of the bulk field. This mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads to Kibble Zurek type scaling behavior. For the AdS soliton the system is non-dissipative and has $z=1$, while for the black brane one has dissipative $z=2$ dynamics. We also discuss the features of a holographic model which would describe the non-equilibrium dynamics around quantum critical points with arbitrary dynamical critical exponent $z$ and correlation length exponent $ν$. These analytical results are supported by direct numerical solutions.

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Pallab Basu, Diptarka Das, Sumit R. Das, Krishnendu Sengupta. 2013-09-26. Quantum Quench and Double Trace Couplings. https://doi.org/10.1007/jhep12(2013)070

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